Control with sensors/actuators assigned by Markov chains: transition rates partially unknown

This study investigates systems where the sensors and the actuators are driven by two independent random events so that at any time only a subset of them is activated. The triggering events are modelled by two Markov chains with partially unknown transition rates. The authors derive a systematic control analysis and synthesis framework using theories in Markovian jumping systems and time-delay systems. The results are given in terms of the delay bounds and the transition probabilities of the Markov chains, which are obtained by using a newly defined Lyapunov-Krasovskii functional and the weak infinitesimal operator. A numerical example is given to demonstrate the effectiveness of the proposed method.